I. Introduction

Semiconductor/liquid junctions provide the best known wet chemical method of converting solar energy into electrical energy or chemical fuels.^1-3 Semiconductor electrodes typically operate with a quantum yield of nearly unity for all energies of light above the absorption threshold of the electrode, which can be in the near-infrared (1.1 eV) or throughout the visible region of the spectrum. The overall energy conversion efficiencies (output power divided by total insolation power striking the front face of the cell under standard conditions) to electrical energy are in excess of 17%, and in some cases, photoelectrodes can provide conversion efficiencies in excess of 10% to chemical fuels, such as water splitting to form H₂ and O₂.^1,4 These systems are therefore extremely promising options for converting the tremendous solar resource (the global average insolation power is 120 000 TW compared to a current global total energy consumption rate of 13 TW)⁵ into energy in a renewable, carbon-neutral fashion.

Despite their success as proof-of-concept devices in the laboratory, much remains to be learned to enable the use of photoelectrodes as a low-cost, globally scalable solar energy conversion technology. Until recently, the fundamental factors that control the transfer of charge across semiconductor/liquid interfaces were relatively poorly elucidated. Additionally, the chemical factors that control recombination of photogenerated carriers at the surface of the solid, and at the solid/liquid contact, are not well-developed. Fundamentally, control over the rate of carriers crossing the interface, relative to the rate at which carriers recombine at the interface, is the key in obtaining chemical control over the properties of photoelectrode-based energy conversion devices. Both of these topics form the basis for the results discussed in this Forum Article.

II. Fundamental Operating Principles of Semiconductor/Liquid Junctions

A. Optical Properties. For the capture and conversion of solar energy, semiconductors possess several key advantages over molecular systems. For many semiconductors, the absorption coefficient is very high, so relatively little material, and relatively little optical depth, is needed to efficiently absorb sunlight.⁶ In addition, unlike molecular absorbers, semiconductors have a continuum of states in both their highest occupied levels (the valence band) and their lowest unoccupied levels (the conduction band), so that the absorption coefficient generally does not decline with increasing excitation energy but instead continually increases above the absorption threshold value defined by the band gap of the semiconductor.

The optimum band gap for absorption of the solar spectrum is well-known and lies between 1.1 and 1.7 eV.⁶ This maximum is produced because photons of energy below the band-gap absorption threshold value will not be absorbed, whereas photons having energies above the threshold will be absorbed but will, in general, rapidly thermalize to produce electron-hole pairs that are nominally the same in energy as those produced by absorption of band-gap energy photons. These two energy-wasting processes form the constraint for optimization of the absorption threshold of any single-threshold system absorbing the solar spectrum incident on the surface of the earth. The optimum efficiency of such a system is 32% for a 1.4-eV band-gap material. The possible efficiency declines relatively slowly for band gaps in the range of 1.1-1.7 eV and then falls rapidly for either smaller or larger band gaps because the band gap either is too large (so that most photons from the sun are not absorbed) or is too small (so that most of the absorbed photon energy is dissipated by thermalization and produces only heat).⁶ Materials such as Si, InP, GaAs, CdTe, and other inorganic semiconductors are therefore of interest as photoelectrodes because such materials have band gaps in the optimal range for solar energy conversion.⁶

B. Energetic Properties. The key energetic properties of a semiconductor are the positions of the top of its valence band, E_vb, the bottom of its conduction band, E_cb, and its Fermi level, E_f (i.e., its electrochemical potential). At absolute zero, the energy of the bottom of the conduction band relative to the vacuum level is the electron affinity of a semiconductor, and the energy of the top of the valence band of a semiconductor is its ionization energy. The difference between E_vb and E_cb is the band gap, E_g, which can be measured optically.

The electrochemical potential, or Fermi level, of a semiconductor can be manipulated by the addition of a small concentration of impurities, i.e., dopants, which form either easily ionizable electrons or easily ionizable electron vacancies (holes) in the semiconductor. The Fermi level is the energy at which statistically the probability of finding an electron in the solid is 1/2, even though in actuality no electronic levels may have that energy in the band gap of the solid. The flat-band potential, E_fb, in the absence of an electric field in a semiconductor is related to the Fermi level of the semiconductor, E_F, by E_F = qE_fb, where q is the charge of an electron. The difference between E_F and the energy of the bottom of the conduction band, E_cb, in the bulk of the semiconductor is

When the n-type semiconductor is brought into contact with a liquid containing a redox couple having an electrochemical potential qE(A/A^-), where E(A/A^-) is the Nernstian potential of the redox couple consisting of the acceptor, A, and the donor, A^-, charge will flow between the semiconductor and the solution (as depicted in Scheme 1a) until equilibrium is established. After equilibrium has been reached, the Fermi level will be the same everywhere in the system. The value of E_F in the semiconductor will change much more than the value qE(A/A^-) because, for even a dilute concentration of redox species, the solution has far more states per unit energy than does the semiconductor in its band-gap region. As a consequence of this interfacial charge flow, at equilibrium (Scheme 1b) the electrode has an excess positive charge, arising from the ionized dopant atoms in the semiconductor, and the solution has an excess negative charge. The positive charge is spread out over the depletion width, W, while the negative charge is spread over a much narrower region close to the electrode.

Scheme 1. Energy vs Distance for an n-Type Semiconductor in Contact with a Redox Species (A/A-)a a (a and b) Equilibration of the semiconductor Fermi level, EF, with the solution Nernstian potential, E(A/A-), results in a space-charge region with width W, which produces a spatially dependent electric potential drop in the solid. (c) The value of G', the standard free energy change for interfacial charge transfer, is given by G' = Ecb - qE'(A/A-), where E'(A/A-) is the formal reduction potential of the A/A- redox system. The surface and bulk electron concentrations are denoted as ns and nb, respectively. At equilibrium, the electrode potential, E, is such that the Fermi level of the semiconductor, EF, equals qE(A/A-) and ns = nso, where nso is the surface electron concentration at equilibrium of the solid/liquid interface. (d) If a potential is applied such that the junction is biased away from equilibrium, ns is not equal to nso, and a nonzero net current, J, flows across the semiconductor/liquid interface.

The electric field strength in the solid depends on the potential dropped in the solid, which, in turn, is a function of the initial difference in the Fermi level of the semiconductor relative to the value of qE(A/A^-). Because the depletion width, controlled by the doping density in the solid, is typically on the order of hundreds of nanometers and the difference in electrochemical potentials is on the order of 1 eV, the electric field in the solid is as strong as 10⁵ V cm^-1. Under the influence of this electric field, charge carriers (electrons or holes), generated by the absorption of light from photons having energies greater than the band gap of the semiconductor, will be rapidly and effectively separated because the periodic potentials of inorganic semiconductors result in relatively large mobilities of charge carriers (100-1000 cm² V^-1 s^-1) in the solid. Hence, semiconductors are generally extraordinarily effective at both light capture and charge separation, two key processes in any solar energy conversion system.

The limit on the efficiency of such systems is generally determined by the energy that can be extracted from the charge-separated photogenerated electron-hole pairs. In principle, the maximum internal energy that can be extracted from photogenerated electrons is given by the difference between E_cb and E(A/A^-); hence, a design principle is to optimize this difference to the greatest extent possible. In practice, this optimization can be achieved, for a given semiconductor, by varying the electrochemical potential of the redox couple. For example, systematic introduction of electron-donating or electron-withdrawing substituients on a redox species motif can be used to tune the formal potential, E'(A/A^-), into the desired range near the top of the valence band for an n-type semiconductor electrode or near E_cb for a p-type semiconductor electrode.

A series of studies has shown that for well-defined semiconductor surfaces, such as Si and InP in nonaqueous solvents, such a systematic tuning of the redox potential provides a rational method for chemically controlling, and optimizing the strength of, the electric field in the semiconductor.⁷ Hence, this approach allows for control over the maximum energy that can, in principle, be extracted from the photogenerated charge carriers in such systems. For example, a series of substituted viologens, cobaltocenes, or ferrocenes have been generally used for such purposes for Si and InP electrodes in CH₃OH or CH₃CN, respectively.^7,8

The actual energy that is produced by such a semiconductor/liquid contact is, however, not the theoretical energy limit but instead depends on the kinetics of the charge carriers in the photostationary state that is produced as a result of illumination of the solid/liquid interface.⁸ This behavior is simply a manifestation of LeChatelier's principle, in that the photovoltage of such a system must be zero in the dark, as is the case at equilibrium. The charge carriers created in the light will tend to recombine so as to oppose the perturbation of the system due to the absorption of sunlight. Greater light intensities will thus produce a stronger tendency for the system to return to its equilibrium condition.

The relevant kinetics processes of such a system can be broken down into five different categories, as shown in Figure 1. The photogenerated charge carriers can recombine in the bulk of the solid, can recombine in the depletion region, can tunnel through the electric potential barrier near the surface, can thermally surmount the interfacial potential barrier, or can recombine at defects (trap states) at the semiconductor/liquid interface. Each of these processes has its own characteristic kinetics and rate law, and, in principle, each responds differently to the controllable variables of dopant density, temperature, illumination intensity, electric field strength, and purity of the semiconductor crystal.⁷ In some cases, all of the mechanisms except the fundamentally limiting one, rate process J_br, can be suppressed, so that such devices operate at their maximum possible efficiency limit in the photostationary state. In other cases, surface recombination (J_ss) or charge transfer across the interface (J_et) dominates the recombination process of the system. When these currents are significant, these rate processes therefore limit the photovoltage, and the energy conversion efficiency, of the device. The remainder of this paper will discuss recent results that have advanced our understanding of the factors that control the interfacial electron-transfer process, J_et, and that control surface-state-related recombination, J_ss, for selected semiconductor/liquid interfaces.

Figure 1 Recombination pathways of photogenerated charge carriers in an n-type semiconductor-based photoelectrochemical cell. The electron-hole pairs can recombine through a current density in the bulk of the semiconductor Jbr, the depletion region, Jdr, or at defects (trap states) at the semiconductor/liquid interface, Jss. Charges can also tunnel through the electric potential barrier near the surface, Jt, or transfer across the interface, Jet. The bold arrows indicate the favorable current processes in the operation of a photoelectrochemical cell. The hollow arrows indicate the processes described in detail herein.

C. Principles of Charge-Transfer Processes at Semiconductor Photoelectrodes. The electron concentration at the surface of the semiconductor, n_s, is related through a Boltzmann-type relationship to the difference between the potential applied to the electrode, E, and E_fb:

If J is shown to follow eq 3, with knowledge of n_s and [A], the value of k_et can be calculated from the observed steady-state J vs E data. Unlike the situation for metallic electrodes, the relatively small, and controllable, value of the electron concentration at the semiconductor surface affords the ability to avoid redox-coupled mass-transport limitations on the charge-transfer flux even for reactions at optimal exoergicity. Hence, rate measurements at semiconductor electrodes can be performed using simple steady-state methods with dissolved redox species, even for relatively large values of the interfacial charge-transfer rate constant.

III. Chemical Control of Charge Transfer at Semiconductor Photoelectrode Surfaces

For nonadsorbed, outer-sphere redox species, extraordinarily low defect densities at the semiconductor/liquid interface are required to prevent adsorption and surface-state-related reactions from dominating the observed interfacial kinetics processes. This constraint occurs because otherwise charge carriers will be captured by surface states and then transferred to the redox species in solution, precluding observation of the direct electron-transfer process and precluding observation of the first-order dependence of the charge-transfer flux on the concentration of acceptors in the solution as well as on the concentration of electrons at the semiconductor surface.^9,10

A. Rate Constant at Optimal Exoergicity. Carefully prepared (100)-oriented n-type Si/CH₃OH viologen^2+/+ contacts have shown the predicted dependence of interfacial charge-transfer rate constants, k_et, on changes in interfacial free energies, G', for driving forces up to, and slightly beyond, that of optimal exoergicity.¹¹ Importantly, the maximum charge-transfer rate constant was observed to be in the range of 10^-17 cm⁴ s^-1, in accord with theoretical expectations for such processes.¹²

B. Driving-Force Dependence of the Interfacial Charge-Transfer Rate Constant. Measurements at higher driving forces are precluded for Si because redox couples having more positive potentials than the valence band edge of Si oxidize the Si surface and/or induce carrier inversion processes that prevent effecting an increase in the interfacial driving force as the Nernstian potential of the electrolyte is increased.¹³ Similar considerations limit the experimentally accessible range of driving forces for InP electrodes.¹⁴ Such considerations are also expected to complicate kinetics measurements at high exoergicity for other small-band-gap (E_g < 2 eV) semiconducting electrodes.

The metal oxide semiconductor ZnO is an attractive material to mitigate these drawbacks and thereby allow direct investigation of the behavior of k_et at large interfacial exoergicities. The wide band gap of ZnO (3.0 eV) allows for a large variation in the driving force, and ZnO is not susceptible to the oxidation or passivation processes that are prevalent in small-band-gap semiconductors.¹⁵

The dependence of electron-transfer rate constants on the driving force for interfacial charge transfer has been investigated using n-type ZnO electrodes in aqueous solutions.¹⁶ Differential capacitance vs potential and current density vs potential measurements were used to determine the energetics and kinetics, respectively, of the interfacial electron-transfer processes. A series of nonadsorbing, one-electron, outer-sphere redox couples with formal reduction potentials that spanned approximately 900 mV allowed evaluation of both the normal and Marcus inverted regions of interfacial electron-transfer processes. All rate processes were observed to be kinetically first-order in the concentration of surface electrons and first-order in the concentration of dissolved redox acceptors. The band-edge positions of ZnO were essentially independent of the Nernstian potential of the solution over the range of 0.106-1.001 V vs standard calomel electrode (SCE).¹⁶

Figure 2 shows a semilogarithmic plot of k_et vs the standard driving force for interfacial electron transfer, -G'. The rate constant at optimal exoergicity, k_et,max, should be obtained when G' = - and in this data set has a value of (9 ± 2) × 10^-17 cm⁴ s^-1. NMR line-broadening measurements of the self-exchange rate constants performed in the same electrolytes as those used in the interfacial rate constant measurements indicated that the redox couples had reorganization energies, , of 0.64-0.69 eV.¹⁷ A k_et vs G' curve calculated with k_et,max = 10^-16 cm⁴ s^-1 and = 0.67 eV, because that corresponds to the value derived from the self-exchange measurements, has been superimposed on the plot of Figure 2 (solid line).

Figure 2 Plots of the electron-transfer rate constant for [Ru(bpy)3]3+/2+ (with bpy = 2,2'-bipyridine), I, [Os(terpy)2]3+/2+ (with terpy = terpyridine), II, [Os(bpy)3]3+/2+, III, [Os(Me2bpy)3]3+/2+ (with Me = methyl), IV, [Os(bpy)2(MeIm)2]3+/2+ (with Im = imidazole), V, [Os(bpy)2(Im)2]3+/2+, VI, [Os(Me2bpy)2(MeIm)2]3+/2+, VII, and [Os(Me2bpy)2(Im)2]3+/2+, VIII, as a function of the standard driving force, -G' = qE'(A/A-) - Ecb, for the redox systems investigated. The solid line represents the predicted ket vs G' behavior for ket,max = 1 × 10-16 cm4 s-1 and sc = 0.67 eV.

Clearly, the rate constant vs driving-force dependence at n-type ZnO electrodes exhibited both normal and inverted regions, and the data are well-fitted by a parabola generated using the classical Marcus theory with a reorganization energy of 0.67 eV. The agreement between the reorganization energy of the ions in solution, obtained from the self-exchange measurements, and the reorganization energy for the interfacial electron-transfer processes, deduced from the rate constant vs driving-force data, indicates that the ZnO/H₂O interface contributed relatively little to the reorganization energy of the overall electron-transfer process and that the reorganization energy was dominated by the redox species in the electrolyte, as expected from an application of the Marcus theory to semiconductor electrodes.

C. Reorganization Energy Dependence. Another theoretical prediction of outer-sphere electron-transfer theories is that the charge-transfer rate constant should depend on the reorganization energy of the species involved in the reaction.^2,18,19 For a self-exchange electron-transfer process, both of the reactants are molecules and hence both can contribute to the reorganization energy. For an electrode process, to first order the reorganization energy of the semiconductor can be neglected, and the reorganization energy should be dominated by the reorganization of the redox acceptor species in the solution.

To evaluate this prediction, a series of compounds having similar formal reduction potentials yet having reorganization energies that spanned approximately 1 eV were prepared and evaluated with respect to their charge-transfer kinetics at ZnO electrodes.¹⁷ The redox couples cobalt trisbipyridine (Co(bpy)₃^3+/2+), ruthenium pentaamine pyridine (Ru(NH₃)₅py^3+/2+), cobalt bis-1,4,7-trithiacyclononane (Co(TTCN)₂^3+/2+), and osmium bis-dimethyl bipyridine bis-imidazole (Os(Me₂bpy)₂(Im)₂^3+/2+) were used for this purpose. Differential capacitance vs potential and current density vs potential measurements were used to measure the interfacial electron-transfer rate constants for this series of one-electron, outer-sphere redox couples. Each interface displayed a first-order dependence on the concentration of redox acceptor species and a first-order dependence on the concentration of electrons in the conduction band at the semiconductor surface, in accord with expectations for the ideal model of a semiconductor/liquid contact. Rate constants varied from 1 × 10^-19 to 6 × 10^-17 cm⁴ s^-1.¹⁷

The outer-sphere reorganization energy of a redox couple at a ZnO electrode, _sc,out, where both the redox couple in solution and the image charge in the semiconductor contribute to the total reorganization energy, is expected to be less than that for the self-exchange reaction of the couple in a homogeneous solution, _se,out. A theoretical value for the outer-sphere reorganization energy of a redox couple at a ZnO electrode can be calculated by^20-22

The inner-sphere reorganization energy at a ZnO electrode is half of the value of that of a self-exchange reaction, _se,in, because half as many molecules participate in each electron-transfer event at an electrode relative to those in a self-exchange process. The total reorganization energy for a redox couple at a ZnO electrode, _sc, is therefore given by _sc = (_se - _se,out)/2 + _sc,out, where _se is the reorganization energy of the self-exchange process.

In the ZnO data for this set of redox species, the interfacial electron-transfer rate constant decreased as the reorganization energy, , of the acceptor species increased.¹⁷ A plot of the logarithm of the electron-transfer rate constant vs ( + G')²/4k_BT (where G' is the driving force for interfacial charge transfer) was linear with a slope of -1 (Figure 3).¹⁷ The rate constant at optimal exoergicity was found to be 5 × 10^-17 cm⁴ s^-1 for this system. The data are thus in excellent agreement with the reorganization energy dependence of interfacial electron-transfer reactions predicted by the Marcus model of interfacial electron transfer at semiconductor electrode surfaces.

Figure 3 Plot of ln ket as a function of the quantity (G' + sc)2/4sckBT for the redox systems investigated. The solid line represents a linear least-squares fit of the data.

D. Driving-Force Dependence. One of the most interesting predictions of electron-transfer theory is the inverted region, in which an increase in the driving force produces a decrease in the electron-transfer rate constant.^23,24 The inverted region has been observed experimentally for both intermolecular and intramolecular donor-acceptor (D-A) systems.^25-27 For electrochemical systems, the electron-transfer rate constant from an individual electronic level in an electrode should show both normal and inverted region behavior, in close analogy to the behavior of molecular D-A systems. However, the observed rate of electron transfer from a metal electrode to an acceptor in solution is a summation of the individual electron-transfer rates from the collection of closely spaced occupied electronic levels in the metal. The observed interfacial current will therefore be dominated by the electronic states that transfer electrons at optimum exoergicity, so for metal electrodes, the total rate will not decrease with the driving force and the inverted region cannot be directly observed.

In contrast to metal electrodes, semiconductor electrodes are well-suited to address some of the fundamental predictions of interfacial electron-transfer theories. An ideal semiconductor has no electronic levels in the band-gap region, so only electrons with energies near the conduction band, for an n-type material, can contribute to the cathodic interfacial current flow. As is the case for a molecular D-A system, the interfacial electron-transfer rate constant of conduction-band electrons to an acceptor in solution should therefore increase, reach a maximal value, and then decrease as the driving force of the interfacial charge-transfer reaction is increased.

Unlike a metal electrode, the driving force at a semiconductor electrode cannot be changed by varying the potential of the electrode. This situation occurs because the differential capacitance of a nondegenerately doped semiconductor electrode is much smaller than the differential capacitance of the electrolyte, so essentially all of the applied potential drops across the electrode and not the electrolyte.

A method of changing the driving force is to hold the energetics of the redox couple constant and to change the chemical state of the semiconductor surface. The pH-dependent shift in the band-edge positions of ZnO and other metal oxides is well-known^19,28 and therefore should afford a method to directly investigate the driving-force dependence of the rate constant to a given redox species. The redox couples [Co(bpy)₃]^3+/2+ and [Ru(bpy)₂(MeIm)₂]^3+/2+ (where bpy is 2,2'-bipyridyl and MeIm is 1-methylimidazole) are of specific interest because prior measurements of the band-edge positions at n-type ZnO electrodes indicate that [Co(bpy)₃]^3+/2+ should be in the normal region, whereas [Ru(bpy)₂(MeIm)₂]^3+/2+ should be in the inverted region.¹⁶ The charge-transfer rate constant for [Co(bpy)₃]^3+/2+ is therefore expected to increase, while the rate constant for [Ru(bpy)₂(MeIm)₂]^3+/2+ is expected to decrease as the band-edge position is made more negative, and therefore the interfacial driving force is increased, by increasing the pH of the solution.

In studies of this system, the ZnO/H₂O junctions displayed nearly ideal energetic and kinetics behavior in contact with [Co(bpy)₃]^3+/2+ and [Ru(bpy)₂(MeIm)₂]^3+/2+ in buffered aqueous solutions.²⁹ Differential capacitance measurements showed that when the solution potential was changed by 700 mV, the band edges of ZnO were fixed to within 10 mV at a given pH with respect to SCE. The flat-band potential of the electrode was shown to vary with pH as expected, thereby allowing controlled variation of the driving force by approximately 200 mV for each redox couple. Current density vs potential measurements displayed a first-order dependence on the acceptor and surface electron concentrations, respectively. This behavior allowed for the experimental determination of the interfacial electron-transfer rate constants for such systems.

The interfacial charge-transfer rate constant, k_et, for [Co(bpy)₃]^3+/2+ was observed to increase with increasing pH, while k_et for [Ru(bpy)₂(MeIm)₂]^3+/2+ was observed to decrease with increasing pH (Figure 4).²⁹ Because increases in pH cause increases in the standard driving force for charge transfer, -G', the redox couples [Co(bpy)₃]^3+/2+ and [Ru(bpy)₂(MeIm)₂]^3+/2+ in contact with n-type ZnO are in the normal and inverted regions of electron transfer, respectively. These results are in excellent agreement with theoretical predictions of the free energy dependence of such interfacial electron-transfer reactions.¹⁶ Taken together with the results of the standard driving-force and reorganization energy dependence of k_et, the data offer strong validation of the Marcus-Hush theoretical model of interfacial charge-transfer reactions.^{19-21,23,24,28}

Figure 4 Plots of the electron-transfer rate constant for n-type ZnO as a function of the standard driving force for [Co(bpy)3]3+/2+ (triangles) and [Ru(bpy)2(MeIm)2)]3+/2+ (diamonds) redox couples. The solid line represents the predicted ket vs G' behavior for ket,max = 5 × 10-17 cm4 s-1 and sc = 1.5 eV. The dashed line represents the predicted ket vs G' behavior for ket,max = 5 × 10-17 cm4 s-1 and sc = 0.53 eV.

IV. Chemical Control of Recombination at Photoelectrode Surfaces

Perhaps the most crucial aspect of any solar energy conversion structure is the interface between the light absorber and the charge-carrier collector. All solar energy conversion systems must have such an interface somewhere in the system; otherwise, the light-generated charge carriers will not know which direction to flow and will produce no net current through an external load. In photovoltaic cells, the interface is between the light absorber (the base) and the minority-carrier collector (the emitter), whereas in photoelectrochemical cells, the interface is between the electrode and the electrolyte. This interface is precisely the place at which the periodic potential experienced by charge carriers in the bulk of the solid is disrupted and at which dangling bonds or other chemical states of the system that are not equivalent to those produced in the bulk of the light absorber phase are present. These states generally have electronic levels that are located in the band-gap region and therefore act as recombination sites for photogenerated charge carriers. For these reasons, interface-derived recombination is often the rate-determining recombination process in all but the most perfectly engineered solar energy conversion systems.

The need to control interface recombination is exacerbated in nontraditional solar cell structures. Traditional solar cell designs are planar structures, derived from the original experiments on p-n junctions at Bell Laboratories in the 1950s.⁶ This approach minimizes the junction area per unit of cell area exposed to sunlight and readily allows analytical solutions of the transport of carriers in the structure. Additionally, the formation of planar structures is amenable to well-defined layer-by-layer deposition using physical growth methods that are widely implemented in the semiconductor industry. The most efficient solar cell devices at present are therefore planar structures.

Conceptual advantages could, however, be obtained from nonplanar structures, in that interpenetrating networks of the absorber and charge-collector phases could orthogonalize the directions of light absorption and charge-carrier collection. This orthogonalization would enable the use of less pure, and therefore lower cost, absorber materials because the carriers could still be effectively collected even if they had relatively short lifetimes in the absorber phase. Examples of such structures are dye-sensitized TiO₂-based solar cells,³⁰ bulk heterojunctions formed from interpenetrating networks of organic polymeric materials,³¹ and hybrids thereof. These devices have a much increased junction area per unit of geometric area, and control of junction recombination is therefore even more important in such systems than it is in planar structures. Interface recombination is also a limiting factor in the use of particulate networks of absorber material, such as Si particles, in that collection of carriers will require movement of charge from particle to particle and therefore requires control of interface recombination to have such systems be useful absorber materials.

Despite its importance, relatively little is known about how to chemically control interface recombination. In conventional solar cells, the problem is difficult because the metallurgical junction is buried and therefore not amenable to chemical manipulation or direct spectroscopic investigation. The junction is, however, exposed in dye-sensitized solar cells, interpenetrating networks, and other nonplanar types of structures. These systems therefore offer a good opportunity to explore the extent to which chemical control can be achieved over the crucial interface recombination processes.

Our initial studies in this area have focused on Si interfaces. The two common low-index faces of crystalline Si are the (100) and (111) orientations.³² The (100)-oriented surface is used in electronic devices but is difficult to prepare with well-defined periodic surface atom bonding at room temperature. The (111)-oriented surface can, however, be prepared by wet chemical etches so that it is H-terminated, with every atop Si atom on large atomically smooth terraces terminated by an Si-H bond that is oriented normal to the (111) surface plane.³³ This surface has therefore been the starting point for our studies on how to achieve chemical control over the electrical properties of an important and prototypical semiconductor surface.

The structure and orientation of the H-terminated Si(111) surface has been well established using both infrared spectroscopy and scanning tunneling microscopy (STM). The infrared spectrum of NH₄F(aq)-etched Si(111) surfaces shows a very sharp Si-H stretch that is strongly polarized normal to the surface plane.³³ The STM data show a 1 × 1 structure that is consistent with all of the Si atop sites being H-terminated. In fact, electrical studies have shown that such surfaces are remarkably electrically perfect and have less than one electrically active defect site in every 40 000 000 surface atoms.³⁴

The issue is, however, one of chemical stability. Upon exposure to ambient air, the H-terminated Si surface rapidly oxidizes, and the resulting surface is highly electrically defective.^35,36 Such systems are not well-suited for use in solar energy conversion devices because of the excessive charge-carrier recombination that arises from the defective surface. A goal is therefore to functionalize the Si surface in a fashion that will mimic the nearly ideal surface termination of the H-terminated Si surface, while simultaneously suppressing the surface degradation pathways that limit the lifetime of H-terminated Si systems.

Our studies have focused on the formation of Si-C bonds as a replacement for the less kinetically stable Si-H bonds. On an unreconstructed Si(111) surface, the distance between adjacent Si atop sites is 3.8 Å.³² The van der Waals diameter of methylene groups in self-assembled monolayers of thiols on Au, for example, is 4.5 Å,^37-39 whereas the van der Waals diameter of a CH₃ group is 2.5 Å.⁴⁰ Hence, CH₃ is the only saturated alkane moiety that can, in principle, sterically terminate every atop site on an unreconstructed Si(111) surface. Functionalization with CH₃ groups, and comparison of the properties of CH₃-terminated Si with surfaces terminated with other more sterically demanding alkyl groups, has therefore comprised the bulk of our initial studies on methods to exert chemical control over a prototypical semiconductor surface.^35,38,40-79

The Si-H bonds on a Si(111) surface have approximately the same bond strength as the Si-H bond in alkylsilanes, 80-85 kcal mol^-1.⁶³ Hence, it might be expected that functionalization of the H-terminated Si surface could be readily accomplished by hydrosilation reactions using PtCl₆^2- and other transition-metal hydrosilation catalysts. However, the steric demands imposed by the Si surface generally preclude clean reactions using such catalysts, which involve sterically demanding transition states. Radical-based olefin addition to Si-H bonds has been performed successfully,^67,68,80 but such systems do not offer the option of terminating every atop site because they do not allow introduction of CH₃ termination onto the surface. In fact, the identity of the remaining non-Si-C-terminated atoms on such surfaces has still not been fully elucidated, with some proposals that the unterminated sites are Si-OH bonds⁶⁸ and others perhaps suggesting that Si-H bonds are present in the structures.

To cleanly introduce CH₃ groups onto the Si surface, we developed a two-step Si surface functionalization process, in which the Si-H bonds were first transformed into metastable Si-Cl bonds and then conventional organo-Li or Grignard reagents were used to convert the Si-Cl bonds into Si-C bonds, yielding the desired alkylated Si surfaces (Scheme 2).⁴⁹ The process initially used a weak Cl radical source, PCl₅ in chlorobenzene, with a radical initiator but subsequently has been extended to use Cl₂(g), other Cl radical sources, and other halogens as well, prior to the Si-halogen to Si-C conversion step.

Scheme 2. Two-Step Si Surface Functionalization Processa a Si-H bonds are first transformed into Si-Cl bonds, using either PCl5 in chlorobenzene with a radical initiator or Cl2(g) with UV light, and then converted to stable Si-C bonds using organo-Li or Grignard reagents.

The alkylated Si(111) surfaces have been extensively characterized to identify the chemical composition, spectroscopic properties, and structure of the functionalized Si surface. Such a definition of the surface is necessary to enable a robust structure-function correlation between the chemical state of the surface and its resulting electrical recombination properties. Initial laboratory-level X-ray photoelectron spectroscopic (XPS) studies indicated that Cl was introduced as a result of the PCl₅ treatment and that Cl disappeared, and C was introduced, in the alkylation process.⁴⁹ Additionally, the C level increased as the chain length of the alkyl increased, and high-resolution XPS data of the Si 2p region indicated that the reaction proceeded with no detectable oxidation of the Si surface.⁴⁹ Subsequently, higher resolution XPS studies with greater surface sensitivity, using synchrotron radiation, have confirmed these initial conclusions and have additionally revealed spectroscopic signatures for the surface Si atoms bonded to C, as evidenced by a chemically shifted surface Si signal ascribable to the surface atoms being bonded to the more electronegative C atoms of the alkyl group.⁴⁴ For CH₃ termination, estimates of the coverage of this Si-C-bonded species are nearly a complete monolayer.⁴⁴

Infrared spectroscopic studies have revealed signals for the -CH₃ umbrella mode on CH₃-terminated Si surfaces, and such signals are polarized normal to the surface plane.⁴⁵ Low-energy electron diffraction studies indicate that CH₃-terminated Si(111) surfaces have a 1 × 1 surface structure, consistent with the termination of every Si atop site producing a surface having the same periodicity as that of the underlying bulk Si.⁴¹ STM studies at 77 K have revealed the 1 × 1 structure as well, and additionally STM data at 4 K have revealed the locations of the H atoms in the -CH₃ groups on the surface (Figure 5).⁴⁶ Unlike molecular silanes or alkanes, which would sterically prefer a staggered conformation and a 60 torsional angle of the topmost C-H bonds relative to the underlying Si-Si bonds, interactions between adjacent CH₃ groups are expected to dominate the packing of the CH₃-terminated Si surface and should produce a 30 torsional angle. Consistently, the observed angle is close to 30, but is slightly less than that angle, with the deviation indicating an interaction favoring rotation of the topmost Si-C bond closer to the underlying Si bonds in the bulk of the Si crystal structure.⁴⁶ The general surface structure of the CH₃-terminated Si surface is therefore well-established at the present time, even by comparison to the extensively studied self-assembled monolayer systems such as thiols on Au, Cu, and Ag and alkoxysilanes on SiO₂.

Figure 5 STM studies at 77 K (inset) revealing the 1 × 1 structure and lattice of the underlying Si surface. Data at 4 K reveal the locations of the H atoms (blue dots) and estimated carbon atom positions (white dots) of the -CH3 groups on the surface. The white bar labeled H-H' represents a distance of 0.18 nm and is in good agreement with the internuclear distance between two H atoms of a CH3 group.

The CH₃-terminated Si surface is indeed more stable toward ambient air oxidation than the H-terminated Si surface. XPS experiments have shown the presence of only submonolayer amounts of silicon oxide on such surfaces after over 1 month of exposure to air, whereas H-terminated surfaces form many monolayers of silicon oxide over that same time period.⁴³ Oxidation under anodic current flow due to the formation of photogenerated holes in a photoelectrochemical cell has been shown to be suppressed for H-terminated Si surfaces when ferrocene is the hole acceptor species in dry organic solvents,⁸¹ but oxide formation still occurs in H₂O-containing organic solvents under such conditions, and stable photoelectrochemical cell operation is precluded entirely for H-terminated, n-type Si surfaces in aqueous solutions. In contrast, -CH₃ termination allows extended anodic current to flow across the Si/liquid interface in both water-containing organic solvents with ferrocene as the acceptor and in aqueous solutions with ferrocyanide as the hole acceptor (Figure 6).^47,48 The alkylated Si surface is therefore much more robust toward oxidation than the H-terminated Si surface, in accord with one of the initial goals of the surface modification procedure.

Figure 6 XPS and electrochemical studies of H- and CH3-terminated Si surfaces. (a) XPS spectra of H-terminated Si before (dashed line) and after (solid line) running J vs E curves in aqueous 0.35 M K4Fe(CN)6 and 0.05 M K3Fe(CN)6. (b) XPS spectra of CH3-terminated Si before (dashed line) and after (solid line) running the J-E curves in aqueous 0.35 M K4Fe(CN)6 and 0.05 M K3Fe(CN)6. (c) J-E curves of H-terminated Si in aqueous 0.35 M K4Fe(CN)6 and 0.05 M K3Fe(CN)6. (d) J-E curves of CH3-terminated Si in aqueous 0.35 M K4Fe(CN)6 and 0.05 M K3Fe(CN)6. The legends for parts c and d are the same. The CH3-terminated surface imparts stability to the J-E curves and is more resistant to oxide growth.

A second important set of experiments involves probing the electrical and electronic properties of the alkyl-terminated Si surfaces. Stabilizing the surface toward oxidation is of relatively limited use in such systems if the functionalization process results in a chemically stable, but inherently electrically defective, Si surface. Two sets of experiments have been used to probe these key properties.

One type of experiment involves measurement in ultrahigh-vacuum conditions of the band bending at functionalized Si surfaces. The key property to be determined is the charge in the region of the semiconductor immediately near the surface. When surface states have energies in the band-gap region, they can accept or donate charge to the bulk of the semiconductor (Scheme 3). This process will occur until the Fermi level of the semiconductor is equal to the Fermi level position driven by occupancy of the surface states. In general, this equilibration between the surface and the bulk will produce a net flow of charge either into or out of the semiconductor, with the direction and magnitude depending on the density of the surface states and their energetic location relative to the initial Fermi level position in the bulk of the semiconductor. For silicon oxide on Si, for example, the near-surface region of the Si has a net charge because the surface Si atoms are bonded to the more electronegative oxygen atoms, and therefore such Si atoms are partially ionized and are positively charged. Measurement of the surface band bending requires measurement of several other parameters, all of which are either known or experimentally measurable quantities. The electron affinity and band gap of Si are known, and the energy position of the core-level photoionization of Si is measurable from the XPS data. The work function can be measured in UHV, and therefore the desired quantity, the band bending, as well as the magnitude of any surface dipole, can be deduced. Such measurements have been performed on CH₃-terminated Si and indicate that the band bending in the semiconductor is less than 0.2 eV (Figure 7).⁴¹ Attainment of the so-called "flat-band" position, where little or no charge density is present in the near-surface region of the semiconductor, thus indicates a nearly ideal, covalently terminated surface whose electronic state density is nearly identical with that of the bulk Si.

Scheme 3. Equilibration of the Fermi Level of an n-Type Semiconductor with Surface Statesa a Before equilibration, a large density of surface electric states exist that can accept electrons from the bulk material. Because of the large capacity of these surface states, electrons from the bulk are accepted until the Fermi level equilibrates to the energy determined by the occupancy of the trap states. In this example, the net loss of electrons from the bulk of the semiconductor into the trap states leads to an increase in the depletion region and a relatively large amount of band bending.

Figure 7 Evaluation of the band bending on CH3-terminated Si. Known quantities are Eg = 1.12 eV, bulk = 4.05 eV, EVB - Si 2p (bulk) = 98.74 eV, EVB - EF(bulk) = 1.04 eV, measured quatities are WF = 3.86 eV and EF - Si 2p(surf) = 99.68 eV, and implied values are EVB - EF(surf) = 0.94 eV (i.e., qEFB = -0.1 eV), surf = 3.68 eV, and surf = -0.37 eV.

A second important type of experiment is to measure the rate at which photogenerated charge carriers recombine at the surface of interest. In general, photogenerated carriers can recombine by radiative or nonradiative processes in the bulk of a Si crystal or can recombine at the surfaces. Si exhibits only an extremely weak luminescence signal, however, so another method is needed to conveniently probe the rate of decay of the photogenerated carrier concentration. A suitable method is to monitor the conductivity of the sample in a contactless fashion using either microwave or radio-frequency (rf) conductivity methods. In this approach, the sample is inductively coupled to an rf coil and the reflected power in the rf circuit is monitored as a function of time.³⁴ In a nearly intrinsic sample, the number of charge carriers is relatively low, so the dark baseline conductance is relatively small. Photoexcitation, however, produces a large excess of mobile electrons and holes, and the conductivity of the sample increases significantly. This increased conductance produces a distinctive, measurable signal in the rf coil, and the rate of decay of the signal allows extraction of the rate of decay of the carrier concentration in the sample. For thin (<200 m) Si samples having a long bulk lifetime (>6 ms in float-zone Si), the carriers can decay into the surfaces many times before they will naturally decay in the bulk of the sample. If both of the surfaces are polished and treated chemically equivalently, then when the observed lifetime is shorter than the bulk lifetime, the measured carrier concentration decay rate represents twice the surface decay rate (because two surfaces are simultaneously active in recombination).

The fundamental parameter of interest is the surface recombination velocity, S, which represents the velocity at which carriers that impinge on the surface recombine as a result of surface-state trapping events. The value of S is related to the observed lifetime, _obs, the bulk lifetime, _b, and the sample thickness, d, as

Additionally, assuming that the traps have a geometric cross section for carrier capture, the value of S, in the absence of a strong electric field at the surface, can be related to the effective number of surface traps, N_ss, by

For H-terminated Si samples, the S values are remarkably low and can be less than 0.25 cm s^-1.³⁴ This value indicates that less than 1 atom in every 40 000 000 is electrically defective on such surfaces. However, after even brief exposure to ambient air, the S value increases rapidly, and within 30 min, the surfaces are so defective that carriers recombine at a rate limited only by their diffusion to the surface.^35,36 In contrast, S values for CH₃-terminated Si remain at 10-30 cm s^-1 even after 1 month of exposure to ambient air (Figure 8).³⁵ This behavior indicates that CH₃ termination not only affords chemical stability of the Si surface but additionally produces an electrically nearly defect-free interface.

Figure 8 Time-resolved photoconductivity decay of H-terminated, (111)-oriented, n-type Si in contact with concentrated H2SO4 acid(aq) (- - -) and after exposure to air for 30 min (___). A single-exponential fit to these decays (not shown) yielded a time constant of 491 ms for the H2SO4-immersed sample and 14 ms for the air-exposed sample. Measurements were made under low-level injection conditions (4 × 1013 injected carriers cm-2 into a 190-mm-thick Si sample). Also shown is a time-resolved photoconductivity decay of methylated, (111)-oriented n-type Si in air under high-level injection conditions (2 × 1016 injected carriers cm-2 in a 190-mm-thick substrate after 504 h in ambient air (···). A single-exponential fit to this decay (not shown) yielded a time constant of 342 ms.

The results for CH₃ termination therefore illustrate the power with which chemical control can, in principle, be obtained over the chemical and electrical properties of semiconductor surfaces. At present, the generality of this approach is relatively unexplored. It would be highly desirable, for example, to be able to use relatively impure Si particles as a light absorber material, but doing so would require methods to passivate the surfaces of such particles from recombination while still allowing charge carriers to move between such particles so as to provide a macroscopic net flux of charge carriers to produce a current through an external load. Similarly, at present no analogous approaches exist to robustly passivate GaAs surfaces, which are more complex chemically because of the multiphasic structure of the oxides of Ga and As, as well as elemental As, that can coexist thermodynamically on such surfaces. Without the development of such methods, the use of inexpensive particles and high-contact-area interpenetrating networks of such absorbers in solar energy conversion systems will be very difficult. Hence, based on the principles elucidated using functionalized Si surfaces, these systems present a challenge for inorganic chemists interested in achieving control over the behavior of complex energy conversion systems involved in cost-effective, carbon-neutral, energy production from the sun.

V. Summary

In summary, the basic principles by which semiconductor photoelectrodes convert sunlight into chemical and electrical energy are now reasonably well-understood. Specifically, the studies discussed herein have elucidated the key factors that control the rate of interfacial charge transfer between semiconductor electrodes and outer-sphere, nonadsorbing, redox species. These studies indicate excellent agreement between the experimental results and the predictions of Marcus theory. Verification of the Marcus inverted region, identification of the maximum charge-transfer rate constant for outer-sphere, nonadsorbing redox couples at optimal exoergicity, the role of nuclear reorganization on the value of the interfacial charge-transfer rate constant at semiconductor electrodes, and the effects of pH-induced changes in the driving force on the rates of such systems have all been revealed quantitatively. The understanding of these charge-transfer processes establishes a firm basis for exerting chemical control over the forward and reverse rates of light-induced interfacial charge transfer that are critical to designing high-efficiency solar energy conversion devices from semiconductor photoelectrodes. In contrast, relatively little is understood about how to control the rates of inner-sphere or absorbed species on semiconductor surfaces or how to chemically eliminate deleterious midgap trap sites by making strong chemical bonds to the surface atoms of concern. An example of success in this direction is obtained by alkylation of the (111)-oriented surface of Si, which has been shown to passivate the surface to oxidation as well as to electrical recombination processes. Methylation of Si(111) surfaces additionally provides a method for obtaining improved electrode stability, for exerting control over the interfacial energetics, and for manipulating other key properties of this semiconductor surface. Extending this approach to group III-V materials and to other photoelectrodes of interest, and thereby achieving complete chemical control over the properties of other important photoelectrode interfaces to optimize solar energy conversion properties for the unassisted splitting of water into H₂(g) and O₂(g), remains a key goal of inorganic and surface chemists studying the properties of semiconductor photoelectrodes.

Acknowledgment

We acknowledge NSF Grant CHE-0213589 and the Office of Basic Energy Sciences, Department of Energy, for the sustained support that has made the research discussed herein possible. In addition, the author is extremely indebted to Tom W. Hamann and David J. Michalak for their invaluable help during the preparation of this manuscript.